A directly modulated laser may be used as an optical transmitter that transmits light at a given wavelength. The power (i.e., amplitude) of the laser light is modulated by corresponding modulation of the current used to drive the laser. For example, the optical transmitter may be modulated to carry a wide-band RF signal. In this case, the electrical current that drives or pumps the laser is modulated with the wide-band RF signal.
The use of a directly-modulated laser to carry a wide-band RF signal may result in distortion due to the multiple carrier frequencies of the multichannel RF signal modulating the laser and/or the harmonics produced by the non-linear nature of the laser device. Intermodulation distortion may be produced when two or more signals mix together to form distortion products. Discrete distortion may be produced from only one carrier. Distortion may include even-order distortion and odd-order distortion. In a CATV system, the most significant types of even-order and odd-order distortion products are second-order distortion products and third-order distortion products, respectively. Second-order intermodulation (IM2) distortion products may include, for example, intermodulation products formed by combining signals at frequencies A and B, such as A±B. In a CATV system, the sum of second-order intermodulation products that are present in a particular channel is commonly referred to as composite second order (CSO) distortion. Third-order intermodulation (IM3) distortion products may include, for example, intermodulation products formed by combining signals at frequencies A, B, and C, such as A±B±C, 2A±B. In a CATV system, the sum of third-order intermodulation products that are present in a particular channel is commonly referred to as composite triple beat (CTB) distortion.
The non-linearities of a time independent non-linear element, such as an amplifier, may be modeled as Taylor series expansions or power series expansions of an input signal. For example, the output y of a non-linear amplifier may be described as a Taylor series expansion of an input x:y(x)=C0+C1x+C2x2+C3x3+C4x4+ . . . Ckxk   Eq. 1where C0, C1, C2, C3, C4, . . . Ck are constants representative of the behavior of the non-linear amplifier. The order within the series is determined by the highest power of x in the expansion. The even order (x2n, where n=1, 2, 3 . . . ) terms in the series (e.g., C2x2, C2x4, C2x6, . . . ) represent even order distortion and the odd order (x2n+1 where n=1, 2, 3 . . . ) terms in the series (e.g., C2x3, C2x5, C2x7, . . . ) represent odd order distortion. For example, C2x2 is the second-order term and represents distortion from the first of the even order terms and C3x3 is the third-order term and represents distortion from the first of the odd order terms. When the input x is an RF input, both x and y are time-varying quantities. With an input having two angular frequencies (ω1 and ω2) represented as x=a sin(ω1t)+b sin(ω2t), the second order term C2x2 creates second order distortion products at frequencies 2ω1, 2ω2, ω1−ω2, and ω1+ω2. Because the non-linear element in this case is time independent, the magnitude and phase of these distortion products are not dependent upon the modulation frequency. However, some non-linear elements, such as lasers, have time dependence and thus have distortion characteristics dependent on the frequency of the modulating signal.
Several techniques have been proposed or employed to compensate for distortion by injecting distortion of equal magnitude but opposite phase to the distortion produced by the laser device. For example, a predistortion circuit may be employed to predistort the RF signal being applied to modulate the laser. One such predistortion circuit includes split signal paths—a main or primary signal path and a secondary signal path. A small sample of the RF input is tapped off the main signal path and a distortion generator in the secondary signal path generates distortion (i.e., predistortion). The predistortion is then recombined with the RF signal on the main signal path such that the predistortion is of equal magnitude but opposite sign to the laser-induced distortion.
These predistortion circuits have been proposed or employed using frequency independent magnitude adjustments in the secondary path and even magnitude-phase tilt filters to account for the frequency dependent effects in non-linear elements that have time dependence. However, such existing predistortion circuits may not adequately compensate for the frequency-dependent distortion. Further, other non-linear elements may also contribute to distortion. In an optical system, for example, non-linear elements may include at least the laser, optical fiber and amplifier non-linearities.